A student hangs a uniform picture frame of mass \(M\) by attaching two light strings to its top corners and looping them over a single fixed hook on the ceiling. Due to the different lengths of the strings, the system reaches static equilibrium with string 1 making an angle \(\theta_1 = 60^\circ\) with the horizontal and string 2 making an angle \(\theta_2 = 30^\circ\) with the horizontal.

Which of the following correctly relates the magnitude of the tension \(T_1\) in string 1 to the magnitude of the tension \(T_2\) in string 2, and provides the correct physical justification?